J.P. Morgan Chase & Co. reached a tentative deal this weekend to pay $13 billion to end a number of civil investigations into its sale of mortgage securities before the 2008 financial crisis, but a separate and potentially more serious criminal probe into the bank and its executives will continue.

The Justice Department, convinced it has strong evidence related to the bank's conduct and eager to send a message to Wall Street, rebuffed repeated attempts by J.P. Morgan to settle the criminal investigation without...